Directional radiating system



Oct 1940- F. E. TERMAN z-rr AL DIRECTIONAL RADIATING SYSTEM 5 Sheets-Sheet 1 Filed- Feb. 19, 1938 //7z/e/7 zors Oct. 15, 1940.

F. E. TERMAN ET AL DIRECTIONAL RADIATING SYSTEM Filed Feb. 19, 1938 5 Sheets-Sheet 2 mu... m ld-MM Oct 15, 1940- F. E. TERMAN ET AL 2,218,437

DIRECTIONAL RADIATING SYSTEM Filed Feb. 19, 1938 5 Sheets-Sheet 3 O O o 8 9 l0 DIPOLE 0 1940' F. E. TERMAN ET AL 2,218,487

DIRECTIONAL RADIATING SYSTEM Filed Feb. 19, 1958 5 Sheets-Sheet 4 W 'mz/enzom PM a. TM

A using comparatively short radiating conductors. For the disclosure of our invention we use the Directional antennas of various kinds are well following figures: known in this art. They are of such common use Figure 1a, a ground plan of a multiple ring that some technical expressions applicable to p ype a at yst L, them have been developed. We will use these Figure lb, a plan of asecondmultiple ring pQlyr expressions in setting forth both the objects of ,phase' radiating ystem. f 1U 'our invention and the methods for accomplishing Figure lo, a plan of a combination of the-sysit'. Examples are: half-wave antenna: a single tems shown in Figures 101; andlb showing the I vertical grounded conductor one-half wave length horizontal field pattern of the resultant system. W high; end-fire arra-yz a row of antennas in a Figure a ground P Of Single ring radiline radiating largely in the direction of the line; ating system with vertical directivitygain: the ratio of power required bya vertical Figure 2b, a vector diagram pertainingto'Figdipole antenna to'th-at' required by some other ure la. specified antenna" to produce the same field I Figure lp diagram fifimparingthe i- 0' and satisfactorily used,.we considerit as a con- Figure 5b, a ground plan pertaining to Figure radiating arrays comprising a. plurality of anhorizon, in horizontal patterns which may be cir- 40 tennas of less than-a half wave length high are cul'ar or of a number of other useful patterns,

b The principal object of our invention is to acthe single ring array mathematically for rigorous 501 Patented ot.15,1940 i 2,218,487

UNITED, STATES PIATENTY- omen DI ECTIONAL RADIATING SYSTEM I Frederick Terman and William W. Hansen,

. Stanford University, Calif. 1 a 7 Application February 19, 1938, Serial No. 191,513 a 26 Claims. (01. 250-11) I Our present invention is concerned with radiother systems. Another object is to-produce an- I ating systems for radio transmission. In partenna-s with desired directional characteristics in ticular; it is concerned with antennas that rethe horizontal plane in various patterns as well H strict the radiation largely to directions desired as with vertical directional characteristics.

. strength at a specified distance in a specified dical directivity of the system shown in Figure Zaj rection from theantennas. r v with that of a vertical dipole and a vertical an- 250 Y Probably the commonest form of'antenna used tenna one-half wave length high. for radiation at the'ordinary broadcast frequen- F gure a ground p o a multip r cies where the energy is desired largelyat low e1e-- radiating system having vertical directivity. vations, that is, as nearly as possible-parallel to Figure 4, a ground plan of a second form of the'ground, is a vertical conductor abouta half multiple ring radiating system having both verti wave length high. This type of radiator sends cal and horizontal directivity. V very little energy vertically above it and compara- Figure 5a, a vectordiagram of a form of single tively little at angles above from the horizonring radiating system having both vertical and tal. I Inasmuch as this kind of antenna is widely horizontal directivity.

' venient standard by which the performances of 5a.

others can be judged. The vertical half-wave an- 'gure 6a, a vector diagram of a secondform of tenna has also been supplemented by an enclosing single ring radiating system having both vertical ring of shorter antennas, of the order of oneand horizontal directivity. I 1

3 tenth wave length high which are intended to jFiaire 6b, a ground plan pertaining't'o Figure 35 suppress radiation at high angles from the ground 6a. nd thus to improve thevertical directivity-of the n accomplishing the objectives of our present antenna. invention, radiating arrays are produced which a In addition to the vertical half-wave antenna, restrict the radiation largely to angles near the also; known. These arrays are usually, in circusuch'as a figureeight distribution; We will showlar arrangements of vertical antennas. Arrays of three methods of treating the problem. The first i .one, two, or more concentric circles are known. method considers ring-shaped arrays as combi 45 These arrays areintended to accomplish'directive nationsof a plurality of end-fire arrays excited -5 radiationwithout the use of very high antennas. with polyphase currents. The second treats a, Our present invention isconcerned with the imsingle ring array from a novel vectorial-point of I provement of the circular array type of radiating view for qualitative explanation. The thirdrneth system and the extension of its capabilities. od treats the combinations of endfire arrays and T complish vertical directivity with short antennas. computation, and it produces formulated results 1 Further, we have the object of getting more nearapplicable to complex combinationsof multiple 1y themostdesirable directional characteristics ring antennas with any desired combinationof; thus producing a desired field intensity at a speciphases in excitation. I a fied distance with less power than required by We refer first to Figure 1a which shows a three- 5 phase radiating system. In the system there are three intersecting end-fire arrays marked A-A', BB', and C-C. Each array is composed of seven vertical antennas in a line. Those in array A-A' are numbered from 1 to 7 inclusive. They are spaced a distance of the order of one-half wave length apart for purposes of explanation, but, as we will show later, the optimum spacing is usually different from half a wave length. The antennas may be of any convenient height from about an eighth of a wave length or less to half a wave length or more. The radiation pattern for an end-fire array, once the antenna locations, dimensions, and connections are known, can be calculated by methods known in the prior art. For example, it may approximate the figure 8 shape shown by the line drawn concentric with the array AA'. At the ends there are two large lobes representing a horizontal plan of field strength at the ground level in which the length of a line drawn from the center to the figure 8 line is proportional to field strength at the array in the direction under consideration. At the center there are some small lobes or ears representing radiation in directions transverse to the axis of the array. The relative polarities of the individual antennas are indicated by or signs in the circles. If a indicates at the instant of observation current flowing from the top of the antenna toward the ground, the would indicate current flowing from the ground toward the top. The antenna polarity alternates from one antenna to the next progressing radially. Each of the three arrays are identical in structure and general character and have the same form of radiation pattern.

The radiating system of Figure la. is made by combining the three antennas and exciting them by currents differing in phase by 120 electrical degrees in progressing around the circumference from one array to the next. That is, the currents in A-A' would be 120 ahead, for example, of the currents in B--B' and those in B-B' would lead the currents in CC' by 120. In the arrangement of the antennas on the ground we show them intersecting. ata point common to the centers of all the arrays so the total array appears as a group of concentric rings. This is a convenient and desirable arrangement but it is not necessary. The individual antennas in the several end-fire arrays can be in other than straight lines and the arrays can be arranged intersecting at any desired angle or can be spaced apart so they do not intersect at all. However, the convenience, especially for computation of the design, of the concentric circular arrangement makes it the preferred one. Accordingly we will discuss the system for convenience in terms of the concentric ring arrangement. Looking at any one of the rings of antennas, the two antennas of each of the three phases, for example antennas I and 1, may be thought of as being analogous to two coil sides of each of the three phases of a three-phase, four-pole rotating armature field. The central antenna 4 being common to three phases 120 apart would carry no current so it could be omitted. The combination of the three intersecting antennas produces an array in which the array elements carry currents differing in adjacent elements in such a way that in progressing along any radius, the phase difference between currents in adjacent elements is 180, and in progressing around any ring, the phase diiTerence between currents in adjacent elements is constant and such that the phase differences in progressing once around the array add to 2X360.

The horizontal resultant radiation pattern of the three-phase system at the ground level is roughly circular in shape. The radiation is concentrated largely in a relatively small angle near the horizon somewhat like the radiation of a vertical half-wave radiator but in general with greater concentration at the angles near the horizon.

In Figure lo we have shown a symmetrical circular arrangement of the antennas but precise symmetry is not necessary for satisfactory operation. Neither is it necessary for the rows of antennas to be on straight lines, although this has the advantage of permitting the use of a cable stretched along the line of an array and using the cable to support vertical conductors instead of using a tower at each place an antenna is required. Also the angle between the arrays which for symmetry is 60 may be varied as desired to change the shape of the radiation pattern. The three-phase antenna suggests at once a two-phase arrangement Where it is desired to use fewer antenna connections. A twophase system can have two arrays intersecting at right angles in which case there is a phase advance of 180 electrical degrees in each angular rotation of 90 mechanical degrees, or, for example, with four arrays rotating in phase 90 electrical degrees for each forty-five mechanical degrees of rotation or any other convenient combination of phases with angular rotation.

In Figure 1a the phase of the antenna currents advances 120 electrical degrees in each 60 mechanical degrees of rotation around the circle. Thus the polarity of the antenna 1 at A, 180 from A, is the same as that of antenna I at A. In this arrangement the polarity of the antennas alternates from 1 to 7 so that the polarities on each side of the center antenna are images of those on the other side, that is, the polarities of antennas 3 and 5 are the same, 2 and 6 the same, and so forth. This condition will always be fulfilled where there is a whole number of complete phase rotations in half the circumference of the ring, but if there is, for example, 1 complete phase rotations in half the circumference, the antennas at opposite ends of the diameters will have opposite polarity. There is nothing that requires an even number of phase rotations in one circumference. In fact, arrays having an odd number of rotations are to be desired in some circumstances.

In Figure 1b we show a radiating system having three complete rotations of phase in one circumference of the ring. Starting from A the phase advances 120 to B and so on around'the ring so that in half the circumference the phase advances 360+120+60=180 electrical degrees. To illustrate this We have numbered the real antennas at A as H to M inclusive. We have in Figure 1b antennas on 9 radii. We could have them on 18 radii in which case antennas I 5 to [8 would be real antennas but this is more antennas than is actually needed in a system of this kind. However, the complete end-fire array H to I8 exists in eifect because the fields of the array sections marked B and C combine to produce a field which is the substantial equivalent of that which would be produced by antennas I5 to l8 if they were present.

The principal point to notice in this arrange ment is that the polarities of antennas at opposite ends of a diameter are not the same and known methods do not; in general make it possible to derive a group of antennas together with" their current magnitudes and phases that will produce ference.

' tem.

that instead of-placing the end-fire array; so one of it's antennas is at the center of the system,- fit is placed so the center is between two'ian tennas of opposite phase. This puts the ninecentral-antennas 14 and I9 to'25 inclusive close together. near the center. Any three adjacent antennas; in the inner ring, being excited"120, apart in phase have currents which add to zero,

andbeing close together the radiation from the group of three is practically zero. Accordingly the inner ring of antennas may be omitted. They our'pre-j cise computations, yet to bedescribed, show that the performance of this particular arrangement are shown clotted to emphasize this.

is improved by omitting the inner ringyand still further improved if the ring is left but reversedin polarity at each antenna. These results are not apparent from qualitative considerations. The arrangement shown in Figure lb has an approximately circular horizontal radiation pat tern, and high vertical directivity. Inorder to get horizontal'field patterns of forms other thancircular we combine polyphase systems-'-having.

different numbers of phase rotations per circum- For example, in Figure lo we have combinedthe system shown in Figure 1a with that shown in 'Figure'lb. The circles in Figurelc represent the antennas, shown in Figure 1b and the squares represent the antennas shown in Figure 1 1a..v The horizontal field pattern is indicatedjby i the heart-shaped line Figure 1c.

- mathematically as being proportional to the absolute value of the cosine of halfthe horizontal, angle measured from a specified radius of the sys- It will be'noticed that several antennas are n It is: expressed close together in pairs in Figure 1 and thelogical procedure of combining them in single antennas inwliich the magnitude and phase of the current are: made to serve for both antennas suggests itself. This is best. accomplished by"'redesign'ing the entire system in accordance with theprecise methods we will describe. The angle between'th'e axis of symmetry of the antenna array and the axis of symmetry of the radiation, field pattern can be varied at will by adjusting the phase rela-;. 'tionship between the currents exciting the ante'n I nas represented by squares and those exciting the antennas represented by circles. In" regard to computationsit may be remarked that in general 1' once having described a group'ofjantennas with specified locationsfand current magnitudesand phases, the radiation field pattern"'can be com-';

puted by methods known in thepriorart; but, the

fa prescribed field pattern; We haveinven'ted methods for doing this which are setiorth'later in this specification.

'We have now shown qualitatively. how to get radiating systems having high vertical directivity by considering the systems as combinations of I tend-fire arrays. Before proceding tothegrefine-z ments of computation applicable to these s'ystems I 6'5 fiby a single ring of antennas. Later the general we will show how directivity can be accomplished system will. be developed as a combination of a plurality of ring arrays.

, InFigure 2a we show an arrayoi-antennasdise tributed on the circumference of a circle. We}

1 I willzbegin the discussion of Figure 2a, by: first considering how one might be led to a possible design of antenna. We will assume that the antenna is; toradiate equally in all horizontal directions.

Thatis we desirean-array with no'gobvious pree.

' This proceeds as follows.

' findingthe vector sum. I

vector diagram shown in Figure 2b.

fer-red direction. Perhaps the best form for an initial-'assumptionis a circle. see what can be done with a continuous distribu 7 tion of vertical dipoles arranged in a circular ring'.'. I Since there is to be no preferred direction the cur rent in all antennas must be the same, though A suitthis is not necessarily true of the phases. able current distribution, satisfying these requirements,- is to have the dipole strength vary :as

e i where is the azimuth angle measuredfrom some arbitrary zero and 11. is as yet undetermined except thatit must be an integer. As to the radius of our ring of antennas we may safely guess that if we are to get a. considerable degree of vertical 'directivity the ring must be a wave length or so in diameter.

ray that is likely to have the desired characteristics. A diagram of such an antenna is givenin phases. Then the field due to any given element of the array may be represented by a vector of magnitude determined by the current in the element and ofdirection and phase dependent on, it

the phase of the current in the'antenna and the distance from the element to the observation point. The fields due to all the elements can be represented in the same way and the addition;

necessary to get the resultant field due to the addition'of the individual components can be done by putting'the various vectors end to end and so Let us apply this to the antenna shown in Figure- 2a. Before doing this we must actually select a value of n and also we must select a definite radius.

value. such that, viewed from a distant point on theright, the phases of the elements near the top of the ring, for example antennas 0 and I'Lappear to be constant. Under this condition the difference in the distances of the two antennas isjust compensated by the difference in phaseso the radiations from the two antennas arriveat the'observer in phase. This makes I r=.9562

Finally, for convenience in computation, let us re- 7 place our continuous ring of dipoles by 18 uniformly spaced dipoles numbered from 0 to 1'1 in Figure 2a. The vector addition produces the In the Suppose we arbitrarily take n=6. As for the radius r, suppose we take ,a-

Let us therefore Thus, by purely.quali-' tativearguments we can develop an antenna. ar-

straight section of Figure 2b as we go from elev ment to element along the top of the ring the change i'n'distance is exactly compensated by.

thechanging phase of the antenna currents. As

wego around the ring however the compensation getsless and less complete and finally, near the bottomof the ring, the vector diagram curls up completely. Roughly speaking the top of the ring acts like an end-fire array, and the effects due to the bottom elements practically cancel. The rei sultant radiation is represented by the distance between the two ends of the vector representing the vector sum of the components. Note that the vector in Figure 2b representing the radiation Y contribution of antenna number 9 in FigureZa has been divided into two parts to make the vector diagrarng symmetrical. All. this is I when :the

antenna is viewed from a point distant to the right in Figure 2?). If the observation point is in some other direction the vector diagram looks the same except that it is bodily rotated. Thus, it is evident that such an array will radiate equally well in all horizontal directions. Next it is found that it will also tend to confine the radiation to a horizontal plane by observing that, at angles above the horizontal, the compensation of changes of phase by different distances and different current phase can never be complete and so we can never get a straight section in the vector diagram. This is because, if the observer is above the horizontal, all the differences in distance from the observer to the various array elements are reduced so that differences in phase of radiation from the various array elements are apparent to the observer with the result that the resultant intensity of radiation is reduced. This follows from the condition that the change in current phase between adjacent array elements is just compensated by the difference in distance between adjacent elements in the horizontal plane so the observer on the horizontal receives maximum resultant radiation. When the observer is on the horizontal the difference between the several distances from the observer to the array elements is the same as the distances between the corresponding array elements, but when the observer is above the horizontal, the diiferences between the several distances from the observer to the array elements is less than the distances between the array elements, and it is no longer sufficient to compensate for the differences in current phase between the array elements. At the zenith the differences between the several observer-array distances are nearly zero and the vertical radiation is zero. For intermediate observing positions the successive vectors in the straightest part of a diagram like Fig. 217 will be at an angle to each other and the corresponding radiation less than represented by the diagram in Fig. 2b for the observer on the horizontal. Thus, in Figure 2b the center section of the vector diagram would become concave upward and the distance between ends, which determines the intensity, would be greatly reduced. In fact, it will be found that, for angles much above the horizontal, the intensity is very much reduced. So we see that it is possible to accomplish the desired object of vertical directional radiation using a ring of radiating elements.

Figure 2c shows a graph of the vertical radiation pattern of the array represented by Figure 2a. The line marked array of Figure 2a represents at any angle the field strength as the length of an arrow drawn from the origin out to the line. For comparison the radiation patterns of a half-wave antenna marked M2 and a dipole are also shown. It will be seen that. the line representing Figure 2a. is below that of the half Wave antenna down to angles of 0=about 80 degrees where they cross. This means that the array of Figure 2a concentrates its radiation more at angles near the ground than the half-wave antenna. The single ring of antennas presents a pattern of radiation in vertical planes through its origin that has no ears or loops of radiation pattern at angles near the vertical. All radiation is confined as indicated by the diagram 20.

We have now shown qualitatively two ways of arriving at practical radiating systems having the desired directional characteristics. The methods of computation suggested by our qualitative analysis could of course ultimately be used for purposes of design. However, the great number of variations possible in the dimensions of the arrays, number of rings, number of antennas in each ring, the number of phase rotations in each ring, the magnitudes of the currents, and other variable factors including departures from symmetry and height of antennas make the solution of the problems by the use of mathematical procedure derivable from the prior art too complicated and inaccurate to be fully satisfactory. Therefore, we have searched for a mathematical procedure which can simply and naturally add the efiects of all the currents in an array taking into account phases and any other needed factors. Fortunately, it has been possible to develop such a calculational scheme and this has been described in a form suitable for the present purpose. From this point on, we will use this method entirely, and will not attempt any physical interpretation of the results. Using this method, we now try to find general radiating systems that will confine the radiation to angles near the horizon and will give any desired directivity in azimuth. This is a more general requirement than the one which we have used for our preliminary explanation.

We refer to Physics, vol. 7, No. 12-, December 1936, page 460*, W. W. Hansen and the references cited therein. We start with a slight modification of Equation 12 in the reference cited. Equation 12 follows:

where l and) =mfz-A dt and the Asn are functions defined in the paper cited. Here r is the radius, 0 is the vertical angle and 5 the horizontal angle in spherical polar coordinates with the origin at the surface of the earth and the polar axis vertical.

To control the radiation pattern in the desired manner we have to show that it is in our power to control two things. First, we must be able to make the various f3,n (6) take on any desired value at 0:1r/ 2 in order to control the azimuthal distribution, and second we must be able to make the f3,n (0) drop off rapidly with departure from 9:1r/2. in order to confine the radiation to angles near the horizon.

To find out about f3,n we first examine Am. We note that a considerable simplification will take place if we take 2' such that it has a 2 component vertical, that is, we let all the antennas be vertical or nearly so. Since this would be the normal thing to do in practice We adopt this simplification and thus insure that we need consider only the 2 component of As,n.

Next we observe that the 2 component of A3,n contains a term in e 9 We note that this term can never deviate greatly from unity unless the antenna is a quarter wave or more high. Since an object of our present invention is to avoidhigh antennas we simplifylby approximating' this term by one. If this approximation shouldnot'be good-enough the exact calculation canbe done and will in general indicate a slightly higher. gain. 7

Making use of Write downa detailed expression for f3,n,'t'aking the needed definition v of As from the paper cited.

(3) 1 Me ,,,feacp sin owe where Jn is a Bessel ,function, k=2n/'y,iz the curmin 1..

rent density in the z direction and are the cylindrical coordinate radius and'angle, and the integration is'over the volume'foccupied by the Y antenna. We see that if is varies as some function-of p times e PW then f3,n Willbe zero unless fail vanish. I

I There remains the question of how to make f3,n

' decreasewith departure from the angle \9=1r/2.

In considering this problem we note that Jn is an Thus, if we should take oscillatory function. iz=const. e "Jn(kfp) out to some large radius,

determined by'the area available for the array,. beyond which itfis Zero, and let k"=l then we would find that for 9=1r/2, sin :1 and the integrand in (3) would be just J that is, always positive and for this angle the integral would be 4,

considerable. But'at some other angle we would have sin #Tand'JnUc and JnUCp' sin ,6) would: not stay in phase and. approximately complete, cancellation will occur with the. re.-

' sult thatf3,n will fall off for angles away, from 0=1r/2 that is, theradiation'will decrease at angles away from the horizontal. In re gard to the -mathematical interpretation of maining'integral over p isthe determining one f3,n(0.) and to have the intensity large, the integrand must be large and usually of. the same" jsign, for example when sinfi l, we have the quantities discussed .abovait should be noticed that while values of 9 can be found for which ".J Uc sin 0) is greater than -J (k neither of these quantities determine 13,1109) on which the Rathenit is the integral of their product over the volume of the antenna Which determines fa, n(0). Of this volume integration, the integration over fand the height give intensity depends.

only constants that are not of interest. The re and itinvolves theproduct JnUcsin 0)Jn(lc integrated from =zero out to the radius of the array. Toget this integral, which determines 'p i which is always positive.

perhaps even'zero. v It canbe verified analytically that the above analysis is in general; a correct'one. What isperhaps' not so clearly evident is the observation that it is often profitable to -make. Zc', slightly larger than k. The results of doing-thisare two: first, the maximum value of 13,11 is somewhatdee. creased because even at 0:1r/2ji and;Jn "do-; not I stay instep, and second fan muses more rapidlyas 6 departs from 1r/2. The first effect results in. a slight lowering of the radiation resistance which is oftennot objectionable. The more rapid decrease of however is quite marked and often increasesjthe'possible gain considerably, that is it assists in restricting' the radiaticnto angles neaiq the horizontal, Just how much It and k'j should these. simplifications we now Thuswe see howto make any undesired On the other hand if sin 6 is less; than 1 then we have toin'tegrate something mucn likethe product 10f sin :c and sin .lsc, for example, and'the result will be small,

roughly, however, the largest useful difference is that which makes k'po a uk o differ by aboutj1.8 5] where 0=maximum v: radiusflof antenna, The I sameobservationis applicable to straight line: end fire arrays. If po iS replaced by 20, the-halflength of the array, a difference between Ida; and a [can of lxi'Z-for example increases the gain by a l This improvement can beeffected" in any existing endfire array byreadjusting the phases of the currents inthe antennas. For ex-. ample, in Figure la, considering only the single,

factor 1.81.

array .of antennasl. to :7 inclusive, the'interval. between successive antennas can bereoluced from a half-wave lengthto a third-,wave length and the" phase. difference between successive; antennas changed from 180 to 120... Then the radiation is confined to one direction, and-one of the figure 2Q V eight lobes'shrinks almost to- Zero. This arrangemer t corresponds tolmown practice. By changi.ng;the-phase diiferencebetween successive an- 'tennas.from,12.0 to 1&8" as desired in ourini ventionwthe directional gain is} increased by 2.1 factor LSLmentioned before.

. Thereisa special case under the general scheme tiohg Namely, incase 11. is 1: or more, and es-- V pecially when ,n is. greater than 1,. it is possible to havei finite for values of kp'less than that; I

correspondingto the first maximum of Jn and. zero for largerv values than flThen-a; decrease ofsin 'laway'frorn unity gives arapid falling ofi 1 in fs,n. This isiapplicable1to the single ring an-,{ 5. 1

tenna. Figure his a caseiof thisi -whenn b and the-ring of antennas is put jwhereflcp=fi and the,

maximumvalueof 'J 6 is at about-8.

We are now ready --to consider theeactual de-, f I sign of a few'typical arrays thoughit maybewellf 40 first to .note thatgit is pcssibler for two arraysto I givec' uite different fields and yetgive the, same directional pattern. 'Ihis-.doesnot seem, to be:

well known sowe illustrate with a simple examf ple. i {Suppose wewant an. antenna thatgives5 uniform horizontal coverage.- 5 We can get this,

equallyv well with a field thatis independent- 0f i or, for instance, with a. field thatvvari'es like e t. In the first case the fieldis in phase at all" values of 4; whereas in thesecond the phasevaries v with As will be shown: presently the correspond ingarraysarequite diiierent but the absolute I magnitudeof the field at a large distance is the same.

We passjnow tovariousi-eziamples illustrating the application of :the above ideas to specificcasesi First; 1 suppose we'g want "an antenna. that disv tributesthe radiation uniformly in azimuth'but keeps it near the'horizon. a ere are many ways of dining thisbut .we will explain two thatare a mcreorlessliinitingcases.

:Forthe first of these, let.us tryto get the'field'.

independent of that is ,fa,0 0, all other.f ,n' substantially zero. From the preceding discus} sion we see that if we had a continuous distribu tionof current ofstrength proportional to Jo(k"p) 'up.to somedimitingradiusi' onand zero outside,v

the-n all'fs exceptjfgo willlbe zero, andthis will be large only for angles nearv the horizon. Morecvergit is-pla'in that as to the variation with '9 the larger ag thebetter and infant, by I making 0 sufii ciently large we can confine-the radiation to angles as near the horizon as we choose. Of course, the practical realization of such an array will not have fthecontinuous distribution mentioned above but will hav'e a finite,nu mber"ofi. .l 5

array elements so arranged as to give a sufficiently good approximation to the continuous distribution. Just exactly how this is to be done is really a matter for detailed calculation in any given case but the following rules can be laid down. First, the antennas should be placed in concentric rings. One ring for each maximum or minimum of Jo will be sufficient. The number of elements in each ring depends on how much variation of field strength with azimuth is allowed but in general the number of antennas in any given ring should be somewhat larger than the k' value corresponding to that ring.

As an example, we have drawn Figure 3, which shows the location of array elements in such an antenna. The antennas are represented by small circles containing either a or a These signs indicate the phases of the currents in the successive rings of antennas, which are 180 apart. The currents in all the antennas of each ring are in phase. This antenna uses 22 elements inside a circle of radius 1.39%. If the intensity in the horizontal plane be considered as a function of the azimuth angle, and if this function be expanded in a Fouriers series in multiples of the azimuth angle, the coefficients for amplitude are, in order, 1.00, 0, 0, 0, 0.17, 0,0, 0.19, 0, 0, 0.17, et cetera. That is, if is the azimuth angle, the intensity will be 1+0 cos +0- cos 2+0 cos 3+0.17 cos 4+0 cos 5+0 cos 6+0.19 cos 7 Now, if all the cosine terms had zero coefiicients, we would have complete uniformity of intensity in azimuth, and inasmuch as none of the coefficients after the first are large, and many are zero, it is evident that the field will be almost circularly uniform in horizontal distribution. How effective the array is in confining the radiation to angles near the horizon is perhaps best stated by giving the gain, which is the ratio of the power required by a vertical dipole to the power required by the array in question when both are giving the same signal on the horizon. In the present example the gain is 2.31. This gain can be increased by adding more rings. In this connection the following approximate formula is of value. If m is the number of rings the gain is approximately given by (4) gain=1.17 /m-1/2 and the approximation gets better as m increases.

We now examine another way of keeping the radiation near the horizon and keeping the distribution uniform in azimuth. This time let us make f3,s finite and all other ,f3,n substantially zero. This We can do by making the current vary like e Moreover, let us get the desired 6 dependence of f3,s by confining all the current to a ring somewhere inside the first maximum of J6. Just how far inside is a matter for individual design. To give an idea of what can be done we may note that if the ring is put very near the origin the gain comes out to be 2.06. The general approximate formula for a case of this type is gain .752 /1z. +3 2 where n is the order of the Bessel function used, in this case 6. We may also note that putting the array elements in a small ring results in very small radiation resistance so that in practice one would generally have the ring well out toward the first maximum of the Bessel function. Such a location greatly increases the radiation resistance without serious loss of gain.

Finally we may ask how the continuous distribution is to be approximated by an actual array. Here again more must be known of the i dividual requirements of a. given case but in general the minimum number of antennas in the ring will be of the order of 2n+3. Figure 2a is an array of this type where n=6 and the ring is at radius k =6. Although 18 antennas are shown in Figure 2, the number could be reduced to 15 without seriously reducing the uniformity of the horizontal pattern of radiation. Mathematically this question is best examined by expanding in Fourier series. Such an expansion shows that a ring of l array elements can be considered as a superposition of an infinite number of continuous ring distributions. As far as the angle dependence goes, the expression is correct We want the conditions so that such a current distribution when inserted in Equation 3 will give substantially only one J, namely fSn. The only way this can be done is to make J ln2l| (k J Iii-1| (lo etcetera negligible in. comparison with Jn(kp) where p is the radius of the ring. The crucial term is that with J Inn]. If we make 1 equal to Zn we get Jlnll=Jn- By taking Z larger one can increase the order of the Bessel function J]nl| and since, by hypothesis, kp is inside the first maximum of J increasing the order will decrease the functions. Just how much 1 must exceed 211. is not obvious, but inspection of the tables of functions shows that an excess of 3 will usually be sufiicient.

Before leaving the subject of arrays that have uniform horizontal coverage and which. keep the radiation confined to angles near the horizon we want to mention explicitly that the multiple ring J0 antenna and the single ring Jn antennas discussed above are not the only typesthat work well. As a particular example we may refer to the three-phase array shown in Figure 1a. In the three-phase array, the current distribution approximates Jze The rings of antennas are placed at radii corresponding approximately to the first three maxima and minima of J2. The currents in the rings of antennas differ in phase by 180 from one ring to the next, and in all the rings the currents vary in phase around the rings as e that is, the phase advancing from antenna to antenna around the ring with two complete phase rotations in one circumference of the rings. In this example it will be noted in particular that the rings of antennas are not precisely at the radii corresponding to the maxima and minima of the Bessel function, as can be verified by sealing the drawing and by reference to the published tables. This departure from the optimum mathematical representation can be made without materially decreasing the effectiveness of the arrangement. Also the antennas need not be in exact circles if the ground situation prevents it although a circular placement is preferred. Similarly the array shown in Figure 1b has a current distribution approximating J3e and the array shown in Figure 1c combines the two arrays, one with currents of the type J2e and Jse As a second type of azimuthal pattern to be achieved let us take the one in which the absolute value of the electric field is proportional to lcos Here, as before, there are many ways of achieving the desired result, of which we illustrate only two.

For the first, let us take E as actually proportional to cos 1 the absolute value signs being omitted. This means f3,1=f3,1, all other fa, zero It can be verified that the desired current distribution Will be proportional to J1(Ic cos Taking n 6, k =6 .for definiteness, we find, in

Here'again'the'dustion of liow m'any array ele-' ments' will .be' needed; arises; and, also as-usual,

we} really need to know moredetails of the propo's'ed installation. Howeve'r,. we have illustrated Y a more or less typical array of this type in Fig. 4. -In Fig..4-th'ere' are three rings of antennas "placed at radii prescribed by the first three maxima and minimaof Ji." Each antenna is repre sentedby a .small'circle containing a or a, The currents from ring to ring going out/along a radius differ inphaseiby 1 8Q. In each rin there is a variation of current; proportional to. 'cos 4) progressing from gantenna to antenna around the rings.

j The same result can obtained in other ways. For example, we etejtnat if the field Lat large distancesis proportional to e ,cos the absolute value of the field strength varies in the desired manner, that is; like loos. pl, But

I I a +l) a -1) Thus We get the desired result" by" having fs,1i+1=f3,n 1, all-other f3 nlzero. If nis larger than onewe can get the desired decrease of the f with by using asingle ring of antennas and 'we will work out 'sucha case to illustrate theuse of the single ring'antnna in applications like the present one. Tobe specific, suppose we take 11. =6,l as before, and agree/toput asinglering of antennas at kp=6. Then-toast fsn'we need current density varying like e going around the ring and to get f3,5 we ne'eda variation like, e t. The only point that might be overlooked I is that the part that-varies like e must be relatively stronger than thatvarying like em since can be'developed into a multiplei ring array. The

preferred way would be to-plot' the values of the functions J 5e andJ'zeU combined and to place the antennas at the maximaand minima of the combined function, .and to excite the antennas I with currents varying in accordancewith the applicable current distribution function. Another way that wouldbe wasteful of equipment would beto put rings of antennas asindicated by the maxima and minima-ofiJs 'and rings as indicated by Jr and exciting the Jsorings with currents varying as e andthe J-i 'rings with currents varying as ei .In either arrangementthe currents would differ in ;.phase byfi180 'in1succes- Naturally the gain; in: directivity would be increased by increasing: the number "of siv rings.

rings. v

'As afinal example of how to obtain ahorizontal pattern likely .to be useful in broadcast work we show one array that gives an intensityvariation with azimuth that "is proportional to [14 1.27 cos 0! We note that this corresponds to having more or lessuniform intensity between fir/land 4-1/2 and nearly zero in the other half circle. Now the calculation goes much as before. We have exactly the same way as before, that the current should be'proportional to A vector diagram for accomplishing thisdistri bution is given in Figure 6a. The ground plan of the applicable array and the shape of the horizontal pattern of the radiation field at the surface of the ground (the dotted line) are shown in Figure 6b inwhich the small circles are numbered to correspond to the vectors of Fig ure 6a. Obviously this array could-be expanded into a multiple ring array if desired.

7 It will be evident to those skilled in this ar that our invention canbe practiced in a variety of ways. It is notclosely limited asto dimensions or radiation pattern. It is most conveniently calculated using the mathematical formulation we have described but practical results can be obtained by other methods. Having become aware of -the general character of the antenna arrays practicable for the objects desired, one

' could compute them by the so-called cut and trymethods of computation, or practicalantennas could be found'by a succession of comparative experiments with selected numbers of radiators and selected dimensions, currents and phase angles. Because of this we emphasize that our invention is novel in the results accomplished, the physical delineations, and in the methods of calculation.- In our description of our invention we have shown the antennas arranged in circular rings. This-is the preferred arrangement, but

where a ring has only a few antennas the logical arrangement is with the antennas at the vertices of a regular polygon. For example, in some instances a ring could have as few-as three antennas arranged in a triangle. t is generallydesirable but notnecessary for the antennas to be equally spaced on the circumference of thecircle, or to be arranged in regularpolygons. However when ground limitations or other practical considerations restrict the arrangement, considerable departures from symmetry and regularspacing are permissible. I

The electrical connections of the antennas to the transmitter exciting them can be worked out on the basis of theory and practice already known in the art. Accordingly we do notdeem it necessary toshow wiring diagrams for our inven:

tion.- The resemblance of the circuits used with our inventionto circuits known in the art has been illustrated by a comparison of the polyphase ring of antennas with the {rotating field structure of a polyphase armature. Considering the antennas as analogous to the coil sides in a polyphase motor, the phase .of the currentsv in successive antennas around the-ring, viewed at any instant, advances completing as many com- I plete phase rotations asmay be desired in one circumference o .the'ring. The currentphasing: m ne antenna-array can be accomplishedxby.

the'use of transmissionlines and tuned-circuits of knowntypes adapted. to the particular requirements oithe antenna concerned'f f Having described our invention we claimz.

1.. A directional radiating system comprising at least two groups of approximately.concentrically circularly disposed substantially vertical radiating elements and' .means. for exciting the radiating elements of j the respective groups with currents. whose phases" at jfa'n'yinstant at successive placesaround the circlesprogre'ss in phase.

rotation at least one complete rotation in phase in one circumference of the circle, the numbers of complete phase rotations of the respective groups differing by at least one.

2. A directional radiation system comprising an approximately circular ring of substantially vertical radiating elements and means for exciting said elements with currents which can be derived as the resultants of at least two polyphase currents whose phases at any instant at successive places around the circle progress in phase rotation at least one complete rotation in phase in one circumference of the circle, the numbers of phase rotations of the respective polyphase currents differing by at least one.

3. A directional radiating system comprising a plurality of approximately concentric circular rings of substantially vertical radiating elements the radii of the circular rings being proportional to factors giving alternately maximum and minimum values of a current distribution series representing the currents required to produce the desired radiated field, the currents in the successive rings being of opposite phase, and means for exciting said elements.

4. A directional radiating system comprising a plurality of approximately concentric circular rings of substantially vertical radiating elements the radii of the circular rings being proportional to factors giving alternately maximum and minimum values of a current distribution series representing the currents required to produce the desired radiated field, the currents in the successive rings being of opposite phase and having polyphase rotations around the circumferences of the rings of elements, and means for exciting said elements.

5. A directional radiating system comprising a plurality of approximately concentric circular rings of substantially vertical radiating elements the radii of the circular rings being proportional to factors giving alternately maximum and minimum values of a current distribution series representing the currents required to produce the desired radiated field, the currents in the successive rings being of opposite phase and difiering in phase from one element to the next in the respective rings of elements, and means for exciting said elements.

6. A directional radiating system comprising a plurality of approximately concentric circular rings of substantially vertical radiating elements the radii of the circular rings being proportional to factors giving alternately maximum and minimum values of a current distribution series representing the currents required to produce the desired radiated field, the currents in the successive rings being of opposite phase and varying in magnitude around the rings as a function of the cosine of an azimuthal angle, and means for exciting said elements.

7. A directional radiating system comprising a plurality of approximately concentric circular rings of substantially vertical radiating elements the radii of the rings being proportional to the values of the argument giving successive maxima and minima of a selected Bessel function, and means for exciting'said elements with currents whose phases at any instant at successive places around the circles progress in phase rotation with a number of complete phase rotations in one circumference of the circle equal to the order of the selected Bessel function.

8. A directional radiating system consisting of a row of antennas spaced definite fractions of a wave length apart and means for exciting the antennas with currents which differ in phase between successive antennas by phase angles which are approximately 1.2 times 360 times the value of said fraction of wave length spacing.

9. A directional radiating system consisting of a plurality of rows of antennas, the individual rows being on lines intersecting at specified geometrical angles, and means for exciting the antennas in the individual rows with currents differing in phase between adjacent antenna rows by electrical angles which are twice the corresponding geometrical angles between the rows.

10. A directional radiating system consisting of a plurality of intersecting rows of antennas, the individual rows intersecting at specified geometrical angles, and means for exciting the antennas in the individual rows with currents differing in phase between adjacent antenna rows by electrical angles which are substantially proportional to the corresponding geometrical angles between the rows.

11. A directional radiating system comprising a plurality of antennas placed around the circumference of concentric rings, and means for exciting the antennas with currents which in each ring are 180 degrees out of phase with the currents in the adjacent rings, and which in the elements of each ring differ in phase from one element to the next.

12. A directional radiating system which consists of a plurality of antennas and means for exciting them with currents which vary from one antenna to the next, the distances between adjacent antennas and'the relative magnitudes of the currents in adjacent antennas being proportional respectively to arguments and magnitudes of the Bessels functions corresponding to the frequency and'field pattern of the radiation of the system.

13. A directional radiating system comprising a plurality of radiating elements placed in concentric rings, and means for exciting the radiating elements with currents which difier in phase from one radiating element to the next in each ring, the radii of the said rings being proportional to arguments, and the currents in the radiating elements of successive rings being proportional to the magnitudes of Bessels functions corresponding to the frequency and field pattern of the radiation of the system.

14. A directional radiating system comprising a plurality of vertical radiating elements materially less than one-half wave length high and means for exciting the radiating elements with currents proportional to the magnitudes of Bessels functions corresponding to the frequency and field pattern of the radiation of the system, and the distances between the radiating elements being proportional to the arguments of said Bessels functions.

' 15. A directional radiating system which consists of radiating elements, arranged in a circle of convenient radius, and means for causing currents to flow in the elements in such a way that the phases of the currents at successive radiating elements around the circle differ from one element to the next, the total of the phase angle differences in one circumference of the circle being a multiple of 360 degrees, said multiple being approximately 3 less than 21l' times the ratio of the said radius of said circle to one wave length of the radiation of the system.

16. A radiating system consisting of a ring of Qtennas to the wave length of the c the system.

10 I antennas, and means for exciting each antenna I witha current presenting a'phase displacement radians, n being greater than 3 less than 21rantennas, and means for exciting each antenna with a current presenting a phase displacement in reference to the currents in the adjacent antennas, the phase displacements between adja-';

cent antennas, taken successively,'adding to 21m radians, n being at least equal to 3 less than 21k times the ratio of the radius of said ring of an 17. A radiating system consisting of a ring of in 'reference to the currents in the adjacent antennas, thephase displacements between adjacent antennas, taken successively, adding to 21m times the ratio of the radius of said ring of an I tennas to the wave length of the radiation of means for exciting the antennas with currentsv "suchthat the current distribution in the system approximates the current distribution specified by a Bessels function of order'n timesthe expois, n'ential' of imp, where i= /land is the azithe system.

18. A radiating system'comprising aplurality of antennas arranged in concentric rings and -muthal angle, and where the argumentofithe *Bessels function isk times the radius, with E greater than 21rdivided by the wave length of the radiation. l

19. Aradiating system comprising a plurality of antennas arranged in concentric rings and means for exciting them'with currents such that the currentdistribution in the system approximates the current distribution specified by a Bessels function of org n times the exponential of imp, where i= /1 and 4: is the azimuthal angle, and where the argument of the Bessels function is 70' times the radius, where k is determined by the condition that 70' times the radius of the outermost ring of antennas shall I exceed by approximately 1.8, 21r times that radius divided by the wave length of the radiation.

20. A radiating system comprising a plurality of antennas arranged in concentric rings and means for exciting the antennas with currents 'such that the current distribution in the system approximates the current distribution specified by a Bessels function of order zero where the argument of the Bessels function is k times the radius, with 7c greater than 21r divided by Q the wave length of theradiation.

21. -A radiating system comprising a plurality of antennas arranged in concentric rings and means for exc'itingthe antennaswith currents such that the current distribution in the system approximates the current distribution specified by a Bessels function'of orderv zero where the argument of the Bessels function is k times the radius, and where lcis determined by the condition that k times the radius of the outermost ring of antennas'shall exceed by approximately 1.8, 211' times that radius divided by the wave length of the radiation.

22. A radiating system comprising a plurality of antennas arranged in concentric rings and radiation of Y means for exciting the antennas, the antennas! being so arranged and excited that the currents therein approximate the current distribution specified by a Bessels function of order n times the exponential of' me where i= 1 and em the azimuthal angle where the argument of the .Bessels function is k times the radius, with lc'- greater than k ='21r divided by the wave length of the radiation, is being greater by an amount sufficient to make the radius of the outermost ring of antennas less by substantially one quarter wave length than the radius ofthe'outermost ring of an hypothetical array similar inv all respects except that theargument of the Bessels function is taken as k times the radius.

v23. A radiating system comprising aplurality v of antennas arranged in concentric rings and means for exciting the antennas, the antennas being so arranged and excited that the'currents therein approximate the current distribution specified by a Bessels function of order zero and where the argument of the Bessels function is k times the radius, with k greater than Ic=21r divided by the wave length of the radiation, Ic' being greater by an amountsufficient to make the radius of the outermost ring of antennas less by substantially one quarter wave length than the radius of the outermost ring of an hypothetical array similar in all respects except that the argument of the Bessels function is,

taken as 'k times the radius.

24. A radiating system comprising two concentric rings of antennas and'an antenna at the" center of said rings, and means'for-exciting the antennas with currents which are in phase in the'several antennas ineach respective ring, the

current in the central antenna being in phase with the current inthe outer ring, and the currents in the first ring being of opposite phase, the radii of the two rings being'respectively approximately 0.480and 0.878 of the wave length I of the radiation.

25. A radiating system comprising three concentric rings of antennas and an antenna at the .center of said rings, and means for exciting the antennas with currents which are in' phase in the several antennas in each respective ring, and in whichthe currents in the central antenna and the second ring are in phase and of opposite phase to the currents in the first and third rings,

the radii of the rings being respectively 0.517,

0.947, and 1.37 times the wave length of, the

radiation.

26. A radiating system comprising four concentric rings of antennas and an antenna at the center of said rings, and means for exciting the antennas with currents which are in'phase in the several antennas in each respective ring, and.

in which the currents in the central antenna, and the second and fourth rings are in phase and of opposite phase to the currents in the first and third rings, the radii of the'ringsbeingrespectively 0.536, 0.980, 1.42, and 1.82 times the wave length of the radiation.

FREDERICK E. TERMAN. 

